Modern optical fiber typically comprises an inner glass core surrounded by a glass cladding and a protective plastic jacket. Guidance of electromagnetic waves is achieved by the core having a slightly higher index of refraction than the surrounding cladding.
Electromagnetic waves that propagate in optical fibers may be decomposed in terms of optical fiber modes. Modes can be either (a) bound core modes which have the majority of their energy confined to the vicinity of the core and can propagate over long distances, or (b) cladding modes or radiation modes which are rapidly attenuated. Optical fibers can be classified as single-mode, two-mode, few-mode, or highly multimode depending on the number of bound core modes that they support.
The number of modes increases with the guidance parameter V which is proportional to the product of (a) the ratio of the core diameter .phi..sub.co with respect to the wavelength .lambda. and (b) the numerical aperture NA which is related to the difference between the core and cladding refractive indices n.sub.co and n.sub.cl respectively, i.e., EQU V=.pi.(.phi..sub.co /.lambda.)NA
where EQU NA=(n.sub.co.sup.2 -n.sub.cl.sup.2).sup.1/2.
Typical values for the core diameter are of order 10 .mu.m for single-mode and two-mode or few-mode fiber operating at communications wavelengths of 1300-1550 nm, and 50 .mu.m or 62.5 .mu.m for highly multimode fiber. Whether single-mode or multimode, the cladding diameter has most commonly an overall diameter of 125 .mu.m, and a plastic jacket diameter is typically 250 .mu.m for standard fiber. The glass core is generally doped with germanium to achieve a slightly higher index of refraction than the surrounding cladding by a factor of roughly 1.001. The jacket is generally plastic and is used to protect the core and cladding elements. It also presents an optically discontinuous interface to the cladding thereby preventing coupling modes in the cladding to other adjacent fibers, and usually plays no significant part in the optical behavior of the individual fiber other than the usually rapid attenuation of cladding modes in comparison with bound core modes.
Two-mode fibers have core dimensions of the same order as those for single-mode fibers except that overall the guidance parameter V is slightly larger, e.g., for fibers with a uniform core and cladding indices (known as step index fibers), V is less than 2.4 for single-mode fibers and between 2.4 and 3.8 for two-mode fibers. Note that as well as or use a fiber which is designed to be single-mode at typical telecommunications wavelengths of 1300 nm and 1550 nm will function as two-mode at shorter wavelengths. One can also fabricate fiber with a slightly larger core diameter and/or NA to function as two-mode fiber at the above wavelengths.
As described in the book by Snyder and Love entitled Optical Waveguide Theory published by Chapman and Hall (London, 1983), under the assumptions of longitudinal invariance and small index differences for which the scalar wave equation is applicable, the modal field magnitudes may be written EQU .PSI.(r,.phi.,z)=.PSI.(r,.phi.) exp{i(.beta.z-.omega.t)}
where
.beta. is the propagation constant PA1 .omega. is the frequency PA1 t is time PA1 z is the axial distance PA1 r,.phi. is the polar trans-axial position along the fiber. PA1 where r.sub.11 is the second-mode spot size PA1 f.sub.1 (.phi.) is the rotation of the pattern described by PA1 f.sub.1 (.phi.)=cos(.phi.) or sin(.phi.),
Single-mode fibers support just one order of bound mode known as the fundamental-mode which we denote as .PSI..sub.01, and which is often referred to in the literature as LP.sub.01. The transverse field dependence for the fundamental-mode in the vicinity of the core may be approximated by a gaussian function as EQU .PSI..sub.01 (r,.phi.)=exp{-(r/r.sub.01).sup.2 }
where r.sub.01 is the fundamental-mode spot size. Two-mode fibers support two orders of mode. In addition to the fundamental-mode, two-mode fibers support a second order of bound mode which we denote as .PSI..sub.11, and which is often referred to in the literature as LP.sub.11. The transverse field dependence of the second order modes in the vicinity of the core may be approximated as EQU .PSI..sub.11 (r,.phi.)=r exp{-(r/r.sub.11).sup.2 }f.sub.1 (.phi.)
and the other variables and constants are as described above. The optical fields of second modes spread out further into the cladding, and require fibers with a larger optical fiber core diameter and/or core-cladding index of refraction difference to reduce attenuative effects, compared to fundamental-mode waves, which have less spread in their field patterns, and hence can propagate in optical fibers with smaller core diameters and/or core-cladding index of refraction differences.
While the above equations describe fundamental and second-mode waves in their most common mathematical forms, it is clear to one skilled in the art that other two-mode wave systems are available for separation and aggregation on the basis of modal characteristic, among which (a) the first two Transverse Electric (or Transverse Magnetic) modes of planar waveguides commonly known as TE.sub.0 and TE.sub.1 (or TM.sub.0 and TM.sub.1), (b) two polarizations of a given order of mode such as (i) planar waveguide modes TE.sub.0 and TM.sub.0, and the polarized optical fiber modes known as LP.sub.01 .sup.x and LP.sub.01.sup.y, as well as (c) the higher level modes of the waves described here and in the publications and patents cited herein, all of which are incorporated by reference.
Fiber optic filters are well known in the art, and may be constructed using a combination of optical fiber and gratings. Using fiber of the previously described type, there are several techniques for creating fiber optic gratings. The earliest type of fiber grating-based filters involved gratings external to the fiber core, which were placed in the vicinity of the cladding as described in the publication "A single mode fiber evanescent grating reflector" by Sorin and Shaw in the Journal of Lightwave Technology LT-3:1041-1045 (1985), and in the U.S. patents by Sorin et al U.S. Pat. No. 4,986,624, Schmadel et al U.S. Pat. No. 4,268,116, and Ishikawa et al U.S. Pat. No. 4,622,663. All of these disclose periodic gratings which operate in the evanescent cladding area proximal to the core of the fiber, yet maintain a separation from the core. A second class of filters involve internal gratings fabricated within the optical fiber itself. One technique involves the creation of an in-fiber grating through the introduction of modulations of core refractive index, wherein these modulations are placed along periodic spatial intervals for the duration of the filter. In-core fiber gratings were discovered by Hill et al and published as "Photosensitivity in optical fiber waveguides: Application to reflected filter fabrication" in Applied Physics Letters 32:647-649 (1978). These gratings were written internally by interfering two counter propagating electromagnetic waves within the fiber core, one of which was produced from reflection of the first from the fiber endface. However, in-core gratings remained a curiosity until the work of Meltz et al in the late 1980s, who showed how to write them externally by the split-interferometer method involving side-illumination of the fiber core by two interfering beams produced by a laser as described in the publication "Formation of Bragg gratings in optical fibers by a transverse holographic method" in Optics Letters 14:823-825 (1989). U.S. Pat. Nos. Digiovanni 5,237,576 and Glenn 5,048,913, also disclose Bragg gratings, a class of grating for which the grating structure comprises a periodic modulation of the index of refraction over the extent of the grating. Within this class of in-fiber gratings, most of the art is directed to in-fiber gratings having the Bragg plane of refractive index modulation perpendicular to the principal axis of the core of the fiber optic cable. A new class of grating involves in-fiber gratings with an angular offset in the plane of refractive index modulation. This type of angled grating is referred to as a mode-converting two-mode grating, and, with properly chosen angle, has the property of converting fundamental-mode power into second-mode power and visa versa. Whether internal or external, both types of gratings can be fabricated as short-period gratings, or long-period gratings. Short-period gratings reflect the filtered wavelength into a counter-propagating mode, and, for silica based optical fibers, have refractive index modulations with periodicity on the order of a third of the wavelength being filtered. Long-period gratings have this modulation period much longer than the filtered wavelength, and convert the energy of one mode into another mode propagating in the same direction, i.e., a co-propagating mode, as described in the publication "Efficient mode conversion in telecommunication fibre using externally written gratings" by Hill et al in Electronics Letters 26:1270-1272 (1990). The grating comprises a periodic variation in the index of refraction in the principal axis of the core of the fiber, such variation comprising a modulation on the order of 0.1% of the refractive index of the core, and having a period associated with either short or long-period gratings, as will be described later.
Fiber-optic add-drop filters are a class of filter of particular interest in multi-wavelength communications and sensor systems, and are used for adding a wavelength channel to or dropping a wavelength channel from an optical fiber bus carrying signals consisting of multiple wavelength channels.
Optical fiber couplers are well known in the art, and generally comprise two fibers as described above having their jackets removed and bonded together with claddings reduced so as to place the fiber cores in close axial proximity such that energy from the core of one fiber couples into the core of the adjacent fiber. There are currently two main ways of practicing this coupling, as well as a third less-used technique. The first method is the side-polished coupler, wherein the cladding material from each fiber is removed through a mechanical polishing operation, followed by a bonding of the two polished claddings together to allow evanescent coupling between the fiber cores. Generally, these couplers are fabricated from a pair of single-mode, or a pair of multi-mode fibers. The side-polished class of fiber optic coupler is described in publications "Single-mode Fibre Optic Directional Coupler" by Bergh, Kotler, and Shaw in Electronics Letters, 16(7)(1980), and "Determination of Single-mode Fiber Coupler Design Parameters from Loss Measurement" by Leminger and Zengerle in the IEEE Journal of Lightwave Technology, LT-3:864-867 (1985). A new class of side-polished mode-converting couplers is described in "Highly selective evanescent modal filter for two-mode optical fibers" by Sorin, Kim and Shaw in Optics Letters 11:581-583 (1986). This class of coupler is fabricated by polishing and bonding a single-mode fiber with a two-mode fiber. As will be described later, this mode-converting coupler converts fundamental-mode waves in a single-mode fiber into second-mode waves, which are principally coupled into the two-mode fiber. A second method of fabricating optical couplers is a fused tapered coupler wherein the two fibers are placed in close proximity, heated, and drawn together. The fused tapered class of coupler is described by Hill et al in "Optical fiber directional couplers: biconical taper technology and device applications", Proceedings SPIE 574:92-99 (1985) with analysis of their operation given in Bures, Lapierre, Lacroix "Analyse d'un coupleur bidirectionnel a fibres optiques monomodes fusionnees" in Applied Optics 22:1918-1921 (1983).
The third method of making couplers involves etching the cladding as described in Single-mode power divider: encapsulated etching techniques by Sheen and Giallorenzi in Optics Letters 4(1):29-31 (1979). Because of reciprocity, optical couplers fabricated from single-mode fiber are intrinsically power-splitting reciprocal devices. The most commonly used coupler involves two coupled single-mode fibers and thus is intrinsically a 4 port device. If such a coupler is used to extract the wavelength band reflected by a single-mode grating, then, because of splitting-loss for the two traversals of non-mode-converting coupler (before and after reflection by the grating), a maximum peak power that can be extracted is 25% of the peak power that would be reflected without the coupler in the system. This least loss case involving approximately 6 dB loss is for a 50/50 splitter known as a 3dB coupler. Cascaded couplers of this type are frequently used in single-mode systems, and the losses can become quite high, and increase for each optical coupling event, as computed for one such system in the publication "Analysis of the reflective-matched fiber Bragg grating sensing interrogation scheme" by Ribeiro et al in Applied Optics 36:934-939 (1997).